Abstract
This paper presents a robust optimization model for the design of a supply chain facing uncertainty in demand, supply capacity and major cost data including transportation and shortage cost parameters. We first present a base model that aims to determine the strategic ‘location’ and tactical ‘allocation’ decisions for a deterministic four-tier supply chain. The model is then extended to incorporate uncertainty in key input parameters using a robust optimization approach that can overcome the limitations of scenario-based solution methods in a tractable way, i.e. without excessive changes in complexity of the underlying base deterministic model. The application of the approach is investigated in an actual case study where real data is utilized to design a bread supply chain network. Numerical results obtained from model implementation and sensitivity analysis experiments arrive at important managerial insights and practical implications.









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Alem, J. D., & Morabito, R. (2012). Production planning in furniture settings via robust optimization. Computers & Operations Research, 39, 139–150.
Aryanezhad, M. B., Jalali, S. G., & Jabbarzadeh, A. (2010). An integrated supply chain design model with random disruptions consideration. African Journal of Business Management, 4, 2393–2401.
Assavapokeea, T., Realff, M. J., & Ammonsc, J. C. (2008a). Min–max regret robust optimization approach on interval data uncertainty. Journal of Optimization Theory and Applications, 137, 297–316.
Assavapokeea, T., Realff, M. J., Ammonsc, J. C., & Hongd, I. H. (2008b). Scenario relaxation algorithm for finite scenario-based min–max regret and min–max relative regret robust optimization. Computers & Operations Research, 35, 2093–2102.
Azaron, A., Brown, K. N., Tarim, S. A., & Modarres, M. (2008). A multi-objective stochastic programming approach for supply chain design considering risk. International Journal of Production Economics, 116, 129–138.
Babazadeh, R., & Razmi, J. (2012). A robust stochastic programming approach for agile and responsive logistics under operational and disruption risks. International Journal of Logistics Systems and Management, 13(4), 458–482.
Baron, O., Milner, J., & Naseraldin, H. (2011). Facility location: A robust optimization approach. Production and Operations Management, 20(5), 772–785.
Bashiri, M., Badri, H., & Talebi, J. (2012). A new approach to tactical and strategic planning in production–distribution networks. Applied Mathematical Modeling, 36, 1703–1717.
Ben-Tal, A., & Nemirovski, A. (2000). Robust solutions of linear programming problems contaminated with uncertain data. Mathematical Programming, Series B, 88, 411–424.
Ben-Tal, A., Goryashko, A., Guslitzer, E., & Nemirovski, A. (2004). Adjustable robust solutions of uncertain linear programs. Mathematical Programming, 99(2), 351–376.
Ben-Tal, A., Chung, B. D., Mandala, S. R., & Yao, T. (2011). Robust optimization for emergency logistics planning: Risk mitigation in humanitarian relief supply chains. Transportation Research Part B, 45(8), 1177–1189.
Bertsimas, D., & Sim, M. (2004). The price of robustness. Operations Research, 52(1), 35–53.
Bertsimas, D., & Thiele, A. (2006). A robust optimization approach to inventory theory. Operations Research, 54(1), 150–168.
Bozorgi-Amiri, A., Jabalameli, M. S., & Mirzapour Al-e-Hashem, S. M. (2011). A multi-objective robust stochastic programming model for disaster relief logistics under uncertainty. OR Spectrum, pp. 1–29.
Bozorgi-Amiri, A., Jabalameli, M. S., Alinaghian, M., & Heydari, M. (2012). A modified particle swarm optimization for disaster relief logistics under uncertain environment. The International Journal of Advanced Manufacturing Technology, 60(1), 357–371.
Chen, X., & Zhang, Y. (2009). Uncertain linear programs: Extended affinely adjustable robust counterparts. Operations Research, 57(6), 1469–1482.
Cordeau, J. F., Pasin, F., & Solomon, M. M. (2006). An integrated model for logistics network design. Annals of Operations Research, 144(1), 59–82.
Esmaeilikia, M., Fahimnia, B., Sarkis, J., Govindan, K., Kumar, A., & Mo, J. (2014a). A tactical supply chain planning model with multiple flexibility options: An empirical evaluation. Annals of Operations Research, 1–26.
Esmaeilikia, M., Fahimnia, B., Sarkis, J., Govindan, K., Kumar, A., & Mo, J. (2014b). Tactical supply chain planning models with inherent flexibility: Definition and review. Annals of Operations Research, 1–21.
Fahimnia, B., Farahani, R., & Sarkis, J. (2013). Integrated aggregate supply chain planning using Memetic Algorithm: A performance analysis case study. International Journal of Production Research, 51(18), 5354–5373.
Georgiadis, M. C., Tsiakis, P., Longinidis, P., & Sofioglou, M. K. (2011). Optimal design of supply chain networks under uncertain transient demand variations. Omega, 39, 254–272.
Hatefi, S. M., & Jolai, F. (2014). Robust and reliable forward-reverse logistics network design under demand uncertainty and facility disruptions. Applied Mathematical Modelling, 38(9), 2630–2647.
Jabbarzadeh, A., Jalali Naini, S.G., Davoudpour, H., Azad, N. (2012). Designing a supply chain network under the risk of disruption. Mathematical Problems in Engineering. doi:10.1155/2012/234324.
Jabbarzadeh, A., Fahimnia, B., & Seuring, S. (2014). Dynamic supply chain network Design for the supply of blood in disasters: A robust model with real world application. Transportation Research Part E: Logistics and Transportation Review, 70, 225–244.
Jeong, K. Y., Hong, J. D., & Xie, Y. (2014). Design of emergency logistics networks, taking efficiency, risk and robustness into consideration. International Journal of Logistics Research and Applications: A Leading Journal of Supply Chain Management, 17(1), 1–22.
Klibi, W., Martel, A., & Guitouni, A. (2010). The design of robust value-creating supply chain networks: A critical review. European Journal of Operational Research, 203, 283–293.
Lalmazloumian, M., Wong, K. Y., Govindan, K., & Kannan, D. (2013). A robust optimization model for agile and build-to-order supply chain planning under uncertainties. Annals of Operations Research. doi:10.1007/s10479-013-1421-5.
Melo, M. T., Nickel, S., & Saldanha-da-Gama, F. (2009). Facility location and supply chain management—a review. European Journal of Operational Research, 196, 401–412.
Mirzapour Al-e-hashem, S. M. J., Malekly, H., & Aryanezhad, M. B. (2011). A multi-objective robust optimization model for multi-product multi-site aggregate production planning in a supply chain under uncertainty. International Journal of Production Economics, 134, 28–42.
Mulvey, J. M., Vanderbei, R. J., & Zenios, S. A. (1995). Robust optimization of large-scale systems. Operations Research, 43(2), 264–281.
Najafi, M., Eshghi, K., & Dullaert, W. (2013). A multi-objective robust optimization model for logistics planning in the earthquake response phase. Transportation Research Part E, 49, 217–249.
Pan, F., & Nagi, R. (2010). Robust supply chain design under uncertain demand in agile manufacturing. Computers & Operations Research, 37, 668–683.
Soyster, A. L. (1973). Convex programming with set-inclusive constrains and applications to inexact Linear programming. Operations Research Letters, 21(5), 1154–1157.
Tang, T. S. (2006). Perspectives in supply chain risk management. International Journal of Production Economics, 103, 451–488.
Wang, B., & He, S. (2009). Robust optimization model and algorithm for logistics center location and allocation under uncertain environment. Journal of Transportation Systems Engineering and Information Technology, 9(2), 69–74.
Yu, Ch S, & Li, H. L. (2000). A robust optimization model for stochastic logistic problems. International Journal of Production Economics, 64, 385–397.
Zhang, Z. H., & Jiang, H. (2014). A robust counterpart approach to the bi-objective emergency medical service design problem. Applied Mathematical Modelling, 38(3), 1033–1040.
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Zokaee, S., Jabbarzadeh, A., Fahimnia, B. et al. Robust supply chain network design: an optimization model with real world application. Ann Oper Res 257, 15–44 (2017). https://doi.org/10.1007/s10479-014-1756-6
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DOI: https://doi.org/10.1007/s10479-014-1756-6